Scanning SQUID microscope with improved spatial resolution

ABSTRACT

A scanning SQUID microscope for acquiring spatially resolved images of physical properties of an object includes a SQUID sensor arranged in perpendicular to the plane of the object under investigation for detecting tangential component of the magnetic field generated by the object. During scanning of the SQUID sensor over the object under investigation, the position signal from a position interpreting unit, as well as relevant output signals from the SQUID sensor are processed by a processing unit which derives from the data, spatially resolved images of the physical properties of the object. The specific orientation of the SQUID sensor with respect to the plane of the object permits an enlarged area of the SQUID chip on which the modulation and feedback line can be fabricated in the same technological process with the SQUID sensor. Additionally, larger contact pads afforded provide for lower contact resistance and ease in forming contact with bias and read-out wires.

This invention was made with the Government support under ContractNumber MDA 904 99 C 2553 awarded by the National Security Agency. TheGovernment has certain rights in the invention.

FIELD OF THE INVENTION

The present invention is directed to a magnetic scanning device such asa scanning SQUID (Superconducting Quantum Interference Device)microscope; and more particularly to an apparatus and technique forimproving the spatial resolution of the scanning SQUID microscope.

Even more particularly, the present invention relates to a scanningSQUID microscope for acquiring spatially resolved images of physicalproperties of an object where a SQUID sensor is positioned substantiallyperpendicular to a test surface of the object under investigation andwhere the SQUID sensor detects a tangential component of the magneticfield generated by the object. In this manner the spatial resolution ofthe SQUID microscope is not limited to the area of the SQUID sensor.

BACKGROUND OF THE INVENTION

Scanning SQUID microscopes have been developed and used for acquiringspatially resolved images of physical properties of different objects bynon-invasively measuring magnetic properties of materials and devices bymeans of superconducting quantum interference devices, also known asSQUID sensors. Prior magnetic imaging devices using SQUIDS havemaintained spatial resolution on the scale of a millimeter or largerwhich is too large for microscopically resolving images needed insemiconductors/micro-electronics testing. Additionally, these devicesalso required placing samples in a vacuum. Some samples such as liquidsor biological specimens cannot tolerate vacuum, thus it is not practicalto measure sources of biomagnetism which are currently the focus of muchof the existing low spatial resolution SQUID imaging.

U.S. Pat. No. 5,491,411 discloses methods and apparatus for imagingmicroscopic spatial variations in small currents and magnetic fieldscapable of providing measurements of magnetic fields with enhancedspatial resolution and magnetic field sensitivity. However, the devicerequires placing a sample within a dewar which may result in theunwanted destruction of the sample when it is exposed to cryogenicliquid or a vacuum. Arguendo, even if the sample is able to tolerate thevacuum environment or cryogenic medium, introducing the sample into thevacuum or cryogenic space for imaging is a somewhat cumbersome and timeconsuming task.

The problem was at least partially resolved by the apparatus formicroscopic imaging of electrical and magnetic properties of a sampledisclosed in U.S. Pat. No. 5,894,220. The device includes a housinghaving a first portion containing a cryogenic medium and a secondportion enveloping a vacuum space. The cryogenic SQUID sensor isdisposed within the vacuum space and in fluid communication with thecryogenic medium in the housing for heat exchange therewith. The samplefor measurement is positioned outside of the housing, at roomtemperature or higher, and can be “seen” by the SQUID sensor through athin window made in the wall of the housing. The output of the cryogenicSQUID sensor is monitored as it is scanned over the surface of thesample.

Another scanning SQUID microscope is described in the InternationalPublication No. WO 00/20879. In this device, the SQUID sensor is scannedover the surface of the sample under study, particularly electroniccircuit, and the measured data are subjected to spatial filtering andmasking techniques in order to increase the spatial resolution andeliminate noise and edge artifacts in magnetic fields and electric fieldimages of the sample.

In all scanning SQUID microscopes disclosed in the above-mentionedreferences the SQUID sensor loop is oriented to be in a plane parallelto the sample plane so that only the normal component B_(z) of thedetected magnetic field is measured. As shown in FIG. 1, SQUID chip 10secured to the lowermost point of a sapphire tip 12 (attached to a tube18) is disposed in parallel with the plane of a sample 14. As the sample14 moves in perpendicular directions X and Y. the SQUID sensor detectsthe magnetic field generated by the sample 14. Particularly, as shown inFIG. 2, a magnetic field B is generated by a current path 16, extendingin this particular example along the axis Y. The SQUID chip 10 disposeddistance Z₀ from the current path 16, detects the normal component B_(z)of the magnetic field B. The problem associated with this techniqueresults from the fact that each acquired data point is the magneticfield averaged over the area of the SQUID sensor projection on thedirection of a scan. Since, as shown in FIG. 3, the whole area of theSQUID sensor 10 faces (downwardly) toward the sample, and the projectionarea of the SQUID sensor onto the sample plane is large, the spatialresolution is then limited to the size of the SQUID sensor projectingonto the sample plane.

The scanning SQUID microscope described in the International PublicationNo. WO 00/20879, slightly improves the spatial resolution by processingthe obtained data through filtering and masking electronics. Thistechnique however requires excessive processing hardware and softwareand includes the limitations associated with parallel orientation of theSQUID sensor to the plane of the sample.

It is known in the prior art to operate SQUID sensors in a negativefeedback loop or flux-locked loop. Referring again to FIG. 1, in orderto couple magnetic flux into the SQUID sensor for maintaining aflux-locked loop, or for applying the read-out flux required for otherimaging schemes, a three-turn coil 20 is wrapped around the sapphire tip12. In order to increase the mutual inductance between the SQUID sensorand the coil 20 it was suggested in U.S. Pat. No. 5,894,220 to fabricatethe coil directly on the SQUID chip using photolithographic printingtechnique known in the art. This suggestion is, however, more difficultin practice, since it requires a larger area of the SQUID that causeslimitations associated with the trade-off between the spatial resolutionand the size of the SQUID chip as discussed in previous paragraphs.

Further, SQUID bias and readout wires 22 are coupled between the SQUIDchip 10 and the processing equipment 24. It is clear to those skilled inthe art, that, as shown in FIG. 1, the contact between the wires 22 andthe SQUID chip 10 is difficult to fabricate. Additionally, due tolimitations applied to the size of the SQUID chip, the contactresistance to the device can be undesirably high if the contact pagesare made too small.

It is therefore clear, that a different approach to the scanning SQUIDmicroscope technique would be desirable to increase spatial resolutionthereof without the necessity of using a rather complex processingtechnique as was proposed in the prior art. The subject system isdirected to removing the limitations associated with the size of theSQUID and to afford a larger size of SQUID chip for accommodatingmodulation and feedback lines, as well as enlarged contact padspositioned thereon.

SUMMARY OF THE INVENTION

It is therefore an object of the present invention to provide a scanningSQUID microscope with enhanced spatial resolution.

It is another object of the present invention to provide a scanningSQUID microscope in which the spatial resolution is not limited by thesize of the SQUID chip.

It is still a further object of the present invention to provide ascanning SQUID microscope in which the SQUID sensor is disposed in sucha way that to achieve a negligible averaging of the detected magneticfield over the area of the SQUID chip in the scanning direction.

It is still another object of the present invention to provide ascanning SQUID microscope in which the SQUID sensor's plane is orientedsubstantially perpendicular to the sample plane in order that theprojection area of the SQUID sensor onto the sample plane is negligible,and the spatial resolution is not limited to the size of the SQUIDsensor.

It is a further object of the present invention to provide a scanningSQUID microscope which detects a tangential component of the magneticfield generated by the object under study due to its orientationsubstantially perpendicular to the plane of the object.

It is yet a further object of the present invention to provide ascanning SQUID microscope in which due to lack of the limitation of thesize of the SQUID chip, the SQUID chip may be fabricated with dimensionswhich permit patterning the modulation and feedback line on the samechip with the SQUID sensor in the same technological process and alsopermits a convenient and low resistance coupling of the bias/read-outwires to the SQUID chip.

According to the teachings of the present invention, a scanning SQUIDmicroscope for acquiring spatially resolved images of physicalproperties of an object takes advantage of a SQUID sensor orientedsubstantially perpendicular to the plane of the object underinvestigation. Specifically, the SQUID sensor is patterned on asubstrate, the plane of which is positioned-in mutual perpendicularrelationship with the surface under test containing the object. In thisorientation, the projection area of the SQUID sensor onto the objectplane is negligible, and the averaging of the detected signals over thearea of the sensor in the scanning direction is negligibly smallcompared to conventional scanning SQUID microscopes where the whole areaof the SQUID sensor faces in a downward orientation to the object underinvestigation. In this manner, the spatial resolution of the SQUIDmicroscope of the present invention is not limited to the size of theSQUID sensor. It has been determined that, for example, at a separationbetween the SQUID sensor and the object, Z=150 microns, the spatialresolution obtained from the SQUID microscope of the present inventionis about 40 microns and 20 microns for the sampling steps of 5 micronsand 2 microns, respectively, while the spatial resolution obtained fromthe conventional SQUID microscope at the same object—SQUID sensorseparation is about 80 microns.

During scanning of the object, the SQUID sensor detects magnetic fieldgenerated by the object at a plurality of positions and delivers asignal corresponding to the tangential component of the magnetic fielddetected.

The scanning SQUID microscope further includes a position interpretingunit for outputting a signal corresponding to a position where magneticfield readings are made. Imaging means are included which receive thesignal from the position interpreting unit as well as the signal fromthe SQUID sensor corresponding to the tangential component of themagnetic field detected from which the imaging means further derive thespatially resolved images of the physical properties of the object.

The SQUID sensor is preferably formed of superconducting YBa₂Cu₃O₇patterned on the substrate made of SrTiO₃ bicrystal., although othersuitable materials known to those skilled in the art are alsoapplicable. The SQUID sensor is attached to a cold-finger tip of themicroscope and in particular to a flat or planar area extending at theend of the tip perpendicular relationship to the surface of the objectunder investigation. The tip is preferably made of sapphire., althoughother thermally conducting non-magnetic materials may be used.

The scanning SQUID microscope includes a housing which has a firstsection containing a cryogenic medium and a second section enveloping avacuum space. A transparent window is formed in the second section ofthe housing for separating the vacuum space from the ambient atmospheresurrounding the housing. The cold-finger tip with the SQUID sensorattached thereto is positioned within the vacuum space, while the objectunder investigation is positioned in ambient surroundings and isseparated from the SQUID sensor by the transparent window. A conduitextends between the first section of the housing and the sapphire tip todeliver the cryogenic medium to the sapphire tip for heat exchange withthe SQUID sensor.

Means are provided in the scanning SQUID microscope for adjusting therelative disposition between the transparent window and the SQUID sensoras well as the distance between the SQUID sensor and the object underinvestigation.

Preferably, the object under investigation is positioned on a scanningstage capable of moving in horizontal X and Y directions mutuallyperpendicular each to the other, and in the Z direction perpendicular toboth the X and Y directions.

With the SQUID chip oriented vertically, the size of the SQUID chip maybe enlarged to permit larger contact areas for the wires coupling theSQUID chip to the processing means thus reducing the contact resistanceto the SQUID. Additionally, due to the specific disposition of the SQUIDchip at the sapphire tip it is much easier to connect the wires to theSQUID chip than known in the prior art.

It is important that due to the orientation of the SQUID chip, as wellas the way it is attached to the sapphire tip of the SQUID microscope, alarger substrate area is permitted for the SQUID chip which also makesit easier to pattern the modulation and feedback line on the samesubstrate with the SQUID chip within the same technological process.

These and other novel features and advantages of the subject inventionwill be more fully understood from the following detailed description ofthe accompanying Drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic representation of a Z-SQUID microscope of theprior art;

FIG. 2 is a schematic representation of the Z-SQUID sensor of the priorart oriented in parallel with regard to the scanning plane of an objectunder investigation;

FIG. 3 is a diagrammatical representation of the magnetic field detectedby the SQUID sensor of the prior art averaged over the area of theZ-SQUID in the direction of a scan;

FIG. 4 shows a longitudinal section of the scanning SQUID microscope ofthe present invention;

FIG. 5 is a schematic representation of the cold-finger sapphire tip ofthe scanning SQUID microscope of the present invention with the SQUIDsensor attached thereto;

FIG. 6 shows schematically the relative disposition between the plane ofthe SQUID sensor of the present invention to the object underinvestigation;

FIG. 7 is a diagrammatical representation of the detected magnetic fieldaveraged over the area of the SQUID sensor projected onto the directionof a scan;

FIG. 8 is a planar view of the surface of the SQUID chip on which theSQUID sensor and modulation/feedback line are patterned in the sametechnological process; and

FIG. 9 is a diagram presenting comparison between the spatialresolutions of the scanning SQUID microscope of the prior art and of thepresent invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring to FIG. 4, a scanning SQUID microscope 30 of the presentinvention includes a housing 32 which accommodates a cryogen containingportion 34 for receiving and holding liquid nitrogen 36, or any othercryogenic medium, as well as a vacuum space 38 which thermally insulatesthe cryogen containing portion 34 from room temperature. The housing 32thus is a modified dewar assembly having the vacuum space 38 maintainedat about 10⁻⁵ Torr. The housing 32 includes an annular plate 40 having acircular opening 42 located substantially in the center thereof. Spacedfrom the annular plate 40, is a window support 44 which supports aplastic flange 46 to the end of which a sapphire window support 48 issecured having an annular opening in which a transparent and thin window50 is attached. The window 50 is preferably formed of sapphire and isapproximately 25 microns thick.

The annular plate 40 is connected via three threaded rods 52 (only twoof which are shown in FIG. 4) to a horizontal adjustment annular disk 54to allow movement of the window 50 with respect to SQUID sensor 56. Theadjustment screws 58 protrude through sides of the annular disk 54 topermit the movement of the window support 44 with respect to the annulardisk 54 for alignment with the window 50 with respect to the SQUIDsensor 56.

A flexible bellows tube 60 for delivery cryogen extends centrally andlongitudinally within the housing 32 and includes stainless steelbellows 62 copper or brass tube 64 and a thermally conducting rodpreferably forming a sapphire tip 66. The stainless steel bellows 62 isin open communication at the end 68 with the cryogen containing portion34 of the housing 32. The end 70 of the bellows 62 is located in thevacuum space 38 and is mounted on the top of interior flange of agrommet 72. The end 74 of the tube 64 is seated and soldered on thebottom of the interior flange of the grommet 72 and thus is in opencommunication with the stainless steel bellows 62. The tube 64 extendsthrough the vacuum space 38 of the housing 32 and further through theopening 42 in the annular plate 40. Located in the second end 76 of thetube 64 and fastened thereto with epoxy is the sapphire tip 66 whichserves as a thermally conducting substrate for the SQUID chip 56. Theend 80 of the sapphire tip 66 as best shown in FIG. 5, is fabricatedwith a flat or planar side surface 82 extending in parallel to thelongitudinal axis of the sapphire tip 66. The SQUID chip 56 isadhesively attached to the flat side surface 82 and is securelymaintained thereon during the operation of the scanning SQUID microscope30.

Referring once again to FIG. 4, the cryogenic medium 36 from the cryogencontaining portion 34 is supplied to the sapphire tip 66 through thestainless steel bellows 62 and the tube 64 to permit heat exchangebetween the SQUID chip and the liquid nitrogen.

The distance between the SQUID chip and the window 50 may be as great as2–3 millimeters or they may be contiguous in relation to each other. Theconstruction of the scanning SQUID microscope 30 permits maintenance ofthe SQUID chip temperature at 77° K while allowing for minute separationbetween the SQUID chip 56 and a room temperature sample 84, alsoreferred herein as the object under investigation.

When the cryogenic liquid passes through the stainless steel bellows 62,and the copper tube 64 these elements may contract. However, suchdeformation will not prevent the position of the sapphire tip 66, northe SQUID chip 56 from being close to the window, due to the fact thatthe window position can be vertically adjusted by means of theadjustment nuts 86.

The sample 84 is positioned outside of the housing 32 of the scanningSQUID microscope 30 on a scanning stage 88 schematically shown in FIG. 4which is capable of movement in the three mutually perpendiculardirections X, Y and Z. Preferably, the stage is motorized and providespositioning accuracy of about one micron or better. The scanning stage88 and mechanism moving such is known to those skilled in the art and isnot described herein in detail. The stage 88 is moved by the steppermotors 90 for driving the stage 88 in X and Y directions. It ispreferable to mount the motors 90 as far as possible from the SQUIDsensor (about 50 cm) and to envelop them in an eddy-current magneticshield in order to shield the SQUID sensor from undesirable magneticfields produced by the motors 90. The motors 90 are mechanically coupledto micrometers. The motors 90 are magnetically noisy, however, steppermotors and micrometers are used since they provide sufficientpositioning accuracy.

Preferably, a computer or processor 92 with controlling software andperipherals for operating the motors is used to operate the scanningstage 88 in the scanning SQUID microscope of the present invention.

In greater detail, the thermally conducting sapphire tip 66 may beapproximately 1″ long with a 0.25″ diameter. The SQUID chip 56 mayconsist of a single 200 nm thick layer 94 of YBa₂Cu₃O₇ patterned on a500 micron thick SrTiO₃ bi-crystal substrate 96, as best shown in FIGS.5 and 8. The SQUID sensor 98 has a generally rectangular shape with theinner hole having widths approximating 10 microns and heightsapproximately 40 microns and with the outer approximate dimensionshaving widths of 30 microns and heights of 60 microns.

The modulation and flux feedback line 100 is patterned near the SQUIDsensor 98 on the same substrate 96 using photolithographic printingtechniques known in the art. After the patterns of the SQUID sensor 98and modulation and feedback line 100 are formed on the substrate 96, thesubstrate 96 is cut into substantially rectangular pieces with thedimensions about 1.5 mm wide and 5 mm long. The SQUID chip 56, is gluedto the sapphire tip 66 with the substrate 96 affixed to the flat sidesurface 82, as best shown in FIG. 5. After the epoxy is cured the end104 of the SQUID chip 56 is polished down to about 800 microns width orsmaller in order that the sapphire tip 66 can be mounted into the window50. During this process, the end 104 of the SQUID chip is polished back,so that the SQUID is as close as possible to the end of the chip,preferably within a few microns.

Fabrication of the modulation and feedback line 100 directly on theSQUID chip provides an increased mutual inductance between the SQUIDsensor 98 and line 100 thus enhancing the magnetic flux coupling intothe SQUID for maintaining a flux-locked loop or for applying theread-out flux required for imaging circuitries of the scanning SQUIDmicroscope of the present invention. It is clear to those skilled in theart that since the substrate 96 is large enough (1.5 mm×5 mm) the areathereon devoid of the SQUID sensor 98 and modulation and feedback line100 constitutes a large enough area to provide larger contact areas 120that makes the contact with bias and read-out wiring 102 easier andsubstantially reduces the contact resistance of the device.

Referring again to FIG. 4, when setting up the microscope for imaging,the window 50 and the end 104 of the substrate 96 are aligned by movingthe window 50 by means of the adjusting nuts 86 or screws 58. Once thewindow 50 is leveled with respect to the SQUID, chip 56, the sample 84on the scanning stage 88 is leveled with respect to the window 50 toinsure that the separation between the sample and the SQUID sensor doesnot change during the scan as well as for achieving a small separationbetween the sample and the SQUID sensor. This operation is performed bymoving the stage 88 in the Z direction shown in FIG. 4, either manuallyor automatically under the control of the computer 92. This operation isknown to those skilled in the art and is not intended to be discussed indetail herein.

To obtain an image of the physical properties of the sample 84,individual raster scan lines are acquired by scanning the sample withthe SQUID sensor in, for example, the X direction while simultaneouslyrecording in the computer 92 the X coordinates (read from themotor-control board 114) and the relevant magnetic field measured (readfrom the SQUID read-out electronics 106). The process is furtherrepeated for the sequence of Y values, by scanning the sample in the Ydirection to construct a 2-dimensional image of the surface of thesample 84.

For example, as shown in FIG. 6, in the case when the sample 84 is amicroelectronic circuitry having a current path 108 the current Iflowing along the current path 108 generates a magnetic field B. TheSQUID chip 56 having its substrate thereof oriented perpendicularly tothe X-Y plane (scanning plane) is positioned a distance Z₀ from thesurface 110 of the sample 84 and is scanned first in the X direction andthen in the Y direction along the surface 110. During the scan, theSQUID sensor detects the tangential component B_(x) of the magneticfield B as opposed to detection of normal component B_(z) of themagnetic field generated by the sample in the scanning SQUID microscopesof the prior art. The spatial resolution of the scanning SQUIDmicroscope depends on the detected magnetic field averaged over the areaof a SQUID sensor projecting onto the sample plane. As best shown inFIGS. 7 and 5, the projection of the SQUID sensor 98 on the samplesurface 110 is negligible and is determined only by the thickness of thelayer of YBa₂Cu₃O₇ deposited onto the substrate 96 of the SQUID chipwhich is approximately 200 nanometers. Therefore, the spatial resolutionin the scanning SQUID microscope of the present invention issubstantially independent of the size of a SQUID chip which permitstaking advantage of a substantially larger area of the SQUID chip, suchas 1.5 mm×5 mm, as opposed to the SQUID chip of the prior art. Due tothe substantially larger area of the SQUID chip it is possible tofabricate the modulation-and-feedback line 100 on the same chip as theSQUID sensor 98. It is also possible to fabricate larger contact pads120 on the substrate 96, thus reducing the contact resistance of thedevice and making the contact with the bias and read-out wires 102easier to implement.

FIG. 7 shows the current density—squared vs. X values in the X directionof scanning when the SQUID sensor scans the sample in the X direction.The spatial resolution is defined as the “whole width at half maximum”(FWHM) of the current density squared peak 112 generated by the currentI flowing through the current path 108. As will be discussed in furtherparagraphs, the spatial resolution of the scanning SQUID microscope ofthe present invention defined as shown in FIG. 7 is higher than thespatial resolution of the conventional scanning SQUID microscope usingthe SQUID chips oriented in parallel to the sample plane.

Referring again to FIG. 4, during the acquisition of the images ofphysical properties of the sample 84, the position of the scanning stage88 is determined by reading positions of the stepper motors 90. Thecontrol program of the computer 92 can read the stepper motor positionsdirectly from a motor controller board 114 which may be mounted in thecomputer 92. Simultaneously, the read-out electronics 106 acquires datafrom the SQUID sensor 98.

Both the SQUID output and the position of the stage 88 are convertedinto digital form and recorded in the computer 92. Once data has beenacquired using a control program of the computer 92, it is convertedinto an image. In its raw 15 form, the image data consists of a set of Nline scans (Y values) intersected with M line scans (X values), with oneor more associated magnetic field values at each of the N×M points. Toprovide an image, the data is first spatially regularized, i.e.,linearly interpolated into rectangular space grids. Then an imagerendering program is used to assign a level of gray to each grid point.The control program is well-known in the art and is not discussed infurther detail. The control program processes the received positionsignals from the motor controller 114, in synchronism with outputs ofSQUID sensor read by the read-out electronics 106 and derives therefromthe spatially resolved images of the physical properties of the object,such as for example magnetic fields emanating from the surface of thesample 84, etc.

Calculations and simulations showing that the spatial resolutionobtained with the SQUID microscope of the present invention is notrestricted to the size of the SQUID chip have been completed. The chartin FIG. 9 shows the comparison of spatial resolution obtained from theSQUID microscope of prior art and the SQUID microscope of the presentinvention. In the chart, the spatial resolution obtained after applyinga magnetic inverse technique, discussed in following paragraphs, isplotted vs. the sample to SQUID separation. The spatial resolution isdefined as the “full width at half maximum” (FWHM) of thecurrent-density-squared peak generated by a current flowing through thewire 108 of the sample 84, as shown in FIG. 6.

In FIG. 9, trace i (horizontal line) corresponds to the spatialresolution of the SQUID sensor with the side dimension˜100 microns.Trace ii shows the spatial resolution from the SQUID microscope of theprior art with data sampling step of 5 microns. It is shown that for theprior art, the spatial resolution is limited to about 80 microns and islimited by the 100 micron size of the SQUID sensor even when the sampleto SQUID separation is reduced to 20 microns. Traces iii and iv show thespatial resolution for the SQUID microscope of the present inventionwith data sampling steps of 5 microns and 2 microns, respectively. Thespatial resolution in the X-direction in these two traces is not limitedby the size of the SQUID. For example, at a separation Z=150 microns,the spatial resolution obtained from the SQUID microscope of the presentinvention is 40 microns and 20 microns for the sampling steps of 5microns and 2 microns respectively, as compared with the spatialresolution obtained from the SQUID microscope of the prior art which isabout 80 microns.

To obtain data plotted in FIG. 9, a magnetic inversion technique wasapplied which permits extraction of the current path from the magneticfield data obtained with the SQUID sensors. The principles of themagnetic inversion technique is based on the Biot-Savart Law, whichrelates current density to magnetic field. The two main magneticinversion techniques are directed to the application of a Fouriertransform and spatial filtering to the measured magnetic field. Thereduction of noise and the edge effect of the data can be eliminated byusing an appropriate signal processing filter such as that disclosed inthe International Publication #WO 00/20879.

In the magnetic inversion technique, it is assumed that the currentpaths are confined in a sheet of thickness d which is much smaller thanthe SQUID-sample separation z. From the Biot-Savart Law, B_(z)=(x,y,z)and B_(x)(x,y,z) are written as follows: $\begin{matrix}{{B_{z}\left( {x,y,z} \right)} \approx {\frac{\mu_{0}d}{4\;\pi}{\int{\int{\frac{{{J_{x}\left( {x^{\prime},y^{\prime}} \right)} \cdot \left( {y - y^{\prime}} \right)} - {{J_{y}\left( {x^{\prime},y^{\prime}} \right)} \cdot \left( {x - x^{\prime}} \right)}}{\left\lbrack {\left( {x - x^{\prime}} \right)^{2} + \left( {y - y^{\prime}} \right)^{2} + z^{2}} \right\rbrack^{3/2}}{\mathbb{d}x^{\prime}}{\mathbb{d}y^{\prime}}}}}}} & (1) \\{{B_{x}\left( {x,y,z} \right)} \approx {\frac{\mu_{0}d}{4\;\pi}z{\int{\int{\frac{J_{x}\left( {x^{\prime},y^{\prime}} \right)}{\left\lbrack {\left( {x - x^{\prime}} \right)^{2} + \left( {y - y^{\prime}} \right)^{2} + z^{2}} \right\rbrack^{3/2}}{\mathbb{d}x^{\prime}}{\mathbb{d}y^{\prime}}}}}}} & (2)\end{matrix}$where μ₀ is the permeability of free space, J_(x) and J_(y) are x and ycomponents of current density, respectively.

The convolution theorem allows Eqs. (1) and (2) to be written in Fourierspace as: $\begin{matrix}{{B_{z}\left( {k_{x},k_{y},z} \right)} = {\frac{{i\;\mu_{0}d}\;}{2}{\frac{{\mathbb{e}}^{{- K}\; Z}}{k}\left\lbrack {{k_{y} \cdot {j_{x}\left( {k_{x},k_{y}} \right)}} - {k_{x} \cdot {j_{y}\left( {k_{x},k_{y}} \right)}}} \right\rbrack}}} & (3) \\{{b_{x}\left( {k_{x},k_{y},z} \right)} = {\frac{\;{\mu_{0}d}\;}{2}{\mathbb{e}}^{{- K}\; Z}{j_{y}\left( {k_{x},k_{y}} \right)}}} & (4)\end{matrix}$where b_(z)(k_(x),k_(y),z), j_(xx)(k_(x),k_(y)) and j_(y)(k_(x),k_(y))are the two-dimensional Fourier transforms of the magnetic field and thecurrent density, respectively. The k_(x) and k_(y) are the components ofthe spatial frequency vector k.

In the case of the SQUID microscope of the prior art, the z-component ofthe magnetic field B(x,y,z) is detected, therefore b_(z)(k_(x),k_(y),z)is the Fourier transform of the data obtained from the prior SQUIDmicroscope. In Eq. (3), j_(x)(k_(x),k_(y)) and j_(y)(k_(x),k_(y)) areunknowns. However, using the conservation of current density, anadditional equation is obtained which allows us to writej_(x)(k_(x),k_(y)) and j_(y)(k_(x),k_(y)) in terms ofb_(z)(k_(x),k_(y),z): $\begin{matrix}{{{j_{z}\left( {k_{x},k_{y},z} \right)} = {{- \frac{i\; 2}{\mu_{0}d}}{\mathbb{e}}^{K\; Z}\frac{k_{y}}{k}{b_{z}\left( {k_{x},k_{y},z} \right)}}},} & (5) \\{{j_{y}\left( {k_{x},k_{y},z} \right)} = {\frac{i\; 2}{\mu_{0}d}{\mathbb{e}}^{K\; Z}\frac{k_{x}}{k}{{b_{z}\left( {k_{x},k_{y},z} \right)}.}}} & (6)\end{matrix}$

The signal processing filters can be applied to the Eqs. (5) and (6) toeliminate undesired noise and edge effect of the data. Taking an inverseFourier the current-density-squared is found which is the sum of eachsquared component.

In the case of X-SQUID microscope of the present invention, thex-component of the magnetic field B_(x)(x,y,z) is detected, therefore,b_(z)(k_(x),k_(y),z) is the Fourier transform of the data obtained fromthe X-SQUID. Eq. (4) is less complicated than Eq. (3) since it has onlyone unknown, j_(y)(k_(x),k_(y)). Then j_(y)(k_(x),k_(y)) in terms ofb_(x)(k_(x),k_(y)) is written: $\begin{matrix}{{j_{y}\left( {k_{x},k_{y},z} \right)} = {\frac{\; 2}{\mu_{0}d}{\mathbb{e}}^{K\; Z}{{b_{x}\left( {k_{x},k_{y},z} \right)}.}}} & (7)\end{matrix}$Signal processing filters can be also applied to Eq. (7) to eliminateundesired noise and edge effects of the data. Specifically from Eq. (2),only the y-component of the current density generates B_(x)(x,y,z), sothe signal from the Fourier transform in Eq. (7) will be mostly alongk_(x)-direction. The appropriate signal processing filter, therefore,maintains the signal along the k_(x)-direction and eliminates theoff-k_(x)-axis signals which are mostly noise. The Inverse Fouriertransform of filtered Eq. (7) permits the obtaining of J_(y)(x,y). Notethat current-density-squared is the square of J_(y)(x,y) for theX-SQUID.

The above analysis assumes that the SQUID is a point sensor so that themagnetic flux linked into the SQUID is just due to the field at oneposition (x,y,z). However, any real SQUID has a non-zero pickup lop areaover which the magnetic field must be integrated to get the total fluxin the SQUID loop. This integration is essentially a process thatresults in the SQUID output being proportional to the average field overthe area of the SQUID loop. In the case of proportional to the averagefield over the area of the SQUID loop. In the case of the z-SQUID, thisaveraging causes blurring of the current sources that is not removed bythe above magnetic inverse technique. In the case of an x-SQUID, howeverthe effect of the blurring due to averaging over the body of the SQUIDcan be removed in the x-direction by replacing Equation (7) above withthe relation:j _(y)(k _(x) ,k _(y) ,z)=2k/[μ₀(e ^(kz)−1)]e− ^(k(z+h)) b _(x)(k _(x),k _(y) ,x)  (8)where b_(x)(k_(x),k_(y),z) is the Fourier transform of the magneticfield averaged over the SQUID loop (which is directly related to theoutput of the SQUID feedback output), h is the height of the SQUID loopin the z-direction, and z is the vertical distance between the currentcarrying region and the closest edge of the SQUID. It is the existenceof the relationship (8) for the x-SQUID which ultimately allows for theproduction of current density images with spatial resolution that arenot completely limited by the SQUID size, as is the case for SQUIDsoriented in the z-direction.

It is therefore clear that due to the orientation of the SQUID sensorsubstantially perpendicular to the plane of the sample under theinvestigation, the enhanced spatial resolution of the imaging isattained wherein the spatial resolution is not limited to the size ofthe SQUID chip. Due to the new structure of the scanning SQUIDmicroscope, not only an increased spatial resolution is obtained, butimprovement to the SQUID sensor itself can be found by fabricatingmodulation and feedback lines directly on the same substrate with theSQUID sensor in one technological process, thus increasing the mutualinductance between the SQUID sensor and the modulation and feedbacklines, as well as simplifying the design of the overall scanning SQUIDmicroscope. Due to the larger area of the SQUID chip, the enlargedcontact pads provide for reduced contact resistance of the device aswell as simplifying the coupling of the bias and read-out wires to theSQUID chip.

Although this invention has been described in connection with specificforms and embodiments thereof, it will be appreciated that variousmodifications other than those discussed above may be resorted towithout departing from the spirit or scope of the invention. Forexample, equivalent elements may be substituted for those specificallyshown and described, certain features may be used independently of otherfeatures, and in certain cases particular locations of elements may bereversed or interposed, all without departing from the spirit or scopeof the invention as defined in the appended claims.

1. A scanning SQUID microscope for acquiring spatially resolved imagesof physical properties of an object, comprising: a SQUID sensorpatterned on a substrate arranged substantially perpendicular to atleast one surface under the test, said object being mounted on saidsurface, said SQUID sensor having a SQUID loop; said SQUID sensordetecting the tangential component B_(x) of a magnetic field generatedby said object in at least one relative position in said at least onesurface under the test and generating an output signal corresponding tothe magnetic field detected at said relative position; and acomputational unit calculating current density j_(y)(k_(x),k_(y),z) as:j _(y)(k _(x) ,k _(y) ,z)=2k/[μ ₀(e ^(kz)−1)]e− ^(k(z+h)) b _(x)(k _(x),k _(y) ,z) where b_(x)(k_(x),k_(y),z) is the Fourier transform of themagnetic field averaged over the SQUID loop, h is a height of the SQUIDloop in the z-direction, and z is the vertical distance between said atleast one surface under the test and an edge of the SQUID closestthereto.
 2. The scanning SQUID microscope of claim 1, wherein saidcomputational unit converts said output signal data to current densitydata, said computational unit including means for providing currentdensity images independent of the dimensions of the SQUID sensor.
 3. Thescanning SQUID microscope of claim 1, wherein said object includes amicroelectronic circuit, and wherein said surface under the testincludes at least one current path generating the magnetic field.
 4. Thescanning SQUID microscope of claim 1, further comprising: (a) positioninterpreting means for outputting a position signal corresponding tosaid at least one relative position; and (b) imaging means for receivingsaid position signal from said position interpreting means, receivingsaid output signal from said SQUID sensor, and deriving therefrom thespatially resolved images of the physical properties of said object. 5.The scanning SQUID microscope of claim 1, further comprising: a scanningstage carrying said object thereon, and means for relocating said objectalong with said scanning stage in at least first and second mutuallyperpendicular directions forming a scanning plane extendingsubstantially perpendicular to said substrate of said SQUID sensor. 6.The scanning SQUID microscope of claim 1, further comprising means foradjusting distance between said SQUID sensor and said at least onesurface under the test of said object.
 7. The scanning microscope ofclaim 1, further comprising modulation/feedback line patterned on saidsubstrate.
 8. The scanning SQUID microscope of claim 1, wherein saidSQUID sensor is formed of superconducting YBa₂CU₃O_(7,) and wherein saidsubstrate is made of SrTiO₃.
 9. The scanning SQUID microscope of claim1, further comprising: a heat conducting tip including a substantiallyflat area extending substantially perpendicular to said surface underthe test of said object, said SQUID sensor being secured to said flatarea of said heat conducting tip.
 10. The scanning SQUID microscope ofclaim 9, further comprising: a housing including a first sectioncontaining a cryogenic medium, and a second section enveloping a vacuumspace; a transparent window formed in said second section of saidhousing and separating said vacuum space from said object disposed inambient atmosphere surrounding said housing, said heat conducting tipwith said SQUID sensor secured thereto being disposed in said secondsection of said housing adjacent to said transparent window; a conduitextending between said first section of said housing and said heatconducting tip to deliver said cryogenic medium thereto for heatexchange with said SQUID sensor; and means for adjusting the relativedisposition between said transparent window and said SQUID sensor.
 11. Amethod for acquiring spatially resolved images of physical properties ofan object generating magnetic field, comprising the steps of:positioning the object on a scanning stage, arranging a SQUID sensorsubstantially in mutually perpendicular relationship between the planethereof and a surface under the test of said object, said SQUID sensorhaving a SQUID loop, scanning said surface under the test of said objectwith said substantially perpendicularly oriented thereto SQUID sensor todetect a tangential component B_(x) of the magnetic field generated bysaid object at a plurality of locations of said surface under the testof said object, processing outputs of said SQUID sensor corresponding tothe B_(x) magnetic field detected at said plurality of locations incombination with respective position signals corresponding to saidlocations, and deriving therefrom the spatially resolved imagesj_(y)(k_(x),k_(y),z) of the physical properties of said object as:j _(y)(k _(x) ,k _(y) ,z)=2k/[μ ₀(e ^(kz)−1)]e− ^(k(z+h)) b _(x)(k _(x),k _(y) ,z) where b_(x)(k_(x),k_(y),z) is the Fourier transform of themagnetic field averaged over the SQUID loop, h is a height of the SQUIDloop in the z-direction, and z is the vertical distance between thesurface under the test and an edge of the SQUID closest thereto.
 12. Themethod of claim 11, further comprising the step of: adjusting distancebetween said SQUID sensor and said object.
 13. The method of claim 12,further comprising the steps of: patterning said SQUID sensor on asubstrate, and patterning a modulation/feedback line on said substratesubstantially simultaneously with said SQUID sensor.